When a player \(i\)  is in \(O_C\)  state then it would like to participate in every group ventures where it might be involved. Optimally, when \(i\)  is surrounded by \(``O"\)  players exclusively, player \(i\)  participates in five public goods games on a square grid. These games are organized by itself and by its neighbors who have also \(``O"\)  attitude. But of course, such a joint venture cannot be forced to a player with \(``A"\)  attitude, therefore the mentioned player \(i\)  must play a prisoner's dilemma game in the latter case. In other words, in an extreme case a player with \(``O"\)  attitude might only play prisoner's dilemma games with its neighbors if it is surrounded by \(``A"\)  attitude players exclusively. The definition of the public goods game agrees with the traditional definition [1]}. Namely, the payoff collected by an \(O_C\)  player from a specific game is \(\Pi = (r \cdot n_{O_C})/ n_{O} - 1\) , where \(n_{O_C}\)  is the number of \(O_C\)  players in the group and \(n_{O}\)  denotes the number of players in the group who have \(``O"\)  attitude. Naturally, the minimal value of \(n_{O}\)  is 2 and it goes up to 5 in the optimal case we mentioned earlier. In case of an \(O_D\)  player the mentioned payoff is \(\Pi = (r \cdot n_{O_C})/ n_{O}\) , because this player does not contribute to the common pool.
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